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5. Hayes Process Macro - Model 4 | #Mediation Analysis with Single Mediator thumbnail

5. Hayes Process Macro - Model 4 | #Mediation Analysis with Single Mediator

Research With Fawad·
5 min read

Based on Research With Fawad's video on YouTube. If you like this content, support the original creators by watching, liking and subscribing to their content.

TL;DR

Use Hayes PROCESS Macro Model 4 to test mediation with one mediator by estimating paths X→M (a), M→Y (b), and X→Y controlling for M (C′).

Briefing

A single-mediator mediation model in Hayes’ PROCESS Macro (Model 4) is used to test whether organizational culture affects organizational performance indirectly through organizational commitment. The core finding is that culture has a statistically significant indirect effect on performance via commitment, and the direct effect remains significant as well—meaning the relationship is best described as partial, not full, mediation. This matters because it identifies commitment as a mechanism linking culture to performance, which can guide interventions aimed at improving outcomes.

The session first lays out mediation terminology: the total effect of an independent variable (X) on a dependent variable (Y) is split into a direct effect (C′) and an indirect effect through a mediator (M). In the notation used, the path from X to M is labeled a, the path from M to Y is labeled b, and the direct effect of X on Y while M is included is labeled C′. The indirect effect is computed as a×b, and the total effect is the sum of the direct and indirect components (C′ + a×b).

With the variables specified—culture as X, commitment as M, and organizational performance as Y—the analysis is run in PROCESS Macro with Model 4 and one mediator. The output is interpreted through two regression equations: one predicting commitment from culture, and another predicting performance from both culture and commitment. Culture significantly predicts commitment (path a), with the model accounting for about 37% of the variance in commitment (R² = .37). Commitment significantly predicts performance (path b), and together culture and commitment account for about 43.13% of the variance in performance (R² = .4313).

For the direct effect, the coefficient for culture predicting performance while commitment is present (C′) is significant (reported as 0.2917), with confidence intervals that do not cross zero. The indirect effect is then calculated by multiplying the relevant path coefficients: a = 0.6041 and b = 0.4531, yielding an indirect effect of about 0.2736. The total effect is reported as the sum of direct and indirect effects, approximately 0.5653. To confirm mediation, the analysis relies on bootstrapped confidence intervals for the indirect effect; because the interval does not include zero, the indirect effect is significant.

Finally, the session distinguishes mediation types. Full mediation would require the direct effect to be non-significant once the mediator is included, indicating culture affects performance only through commitment. Here, the direct effect is significant alongside the indirect effect, so the model indicates partial mediation. The sign of the effects also determines whether mediation is “complementary” or “competitive.” Because the direct and indirect effects share the same positive sign (all relevant coefficients are positive), the mediation is classified as complementary. The results are summarized by reporting the culture → commitment → performance chain, the total effect, direct and indirect effects with confidence intervals and t statistics, and the conclusion that commitment mediates the culture–performance relationship partially.

Cornell Notes

Hayes PROCESS Macro Model 4 is used to test mediation with one mediator: culture (X) → commitment (M) → organizational performance (Y). The indirect effect is computed as a×b, where a is culture→commitment and b is commitment→performance; the direct effect is C′, the effect of culture on performance while commitment is included. In this model, culture significantly predicts commitment (a is significant), and commitment significantly predicts performance (b is significant). Bootstrapped confidence intervals for the indirect effect exclude zero, confirming mediation. Because the direct effect (C′) is also significant, the mediation is partial, and because direct and indirect effects are both positive, it is complementary mediation.

What do a, b, and C′ represent in a single-mediator model, and how do they connect to indirect and total effects?

In the notation used, a is the path from the independent variable X to the mediator M (X→M). b is the path from the mediator M to the dependent variable Y (M→Y). C′ is the direct effect of X on Y when M is included in the model (X→Y controlling for M). The indirect effect is a×b, and the total effect equals C′ + (a×b).

How does the analysis operationalize the mediation model with PROCESS Macro Model 4?

PROCESS Macro Model 4 runs two linked regressions: one predicting the mediator (commitment) from the independent variable (culture), and another predicting the outcome (organizational performance) from both culture and commitment. The output then provides coefficients for the paths (a, b, and C′), model fit summaries (R², F, p), and bootstrapped confidence intervals used to test the indirect effect.

What evidence indicates that culture has a significant indirect effect on performance through commitment?

The indirect effect is computed as a×b using the estimated coefficients (a = 0.6041 and b = 0.4531, giving an indirect effect around 0.2736). Mediation is supported when the bootstrapped confidence interval for the indirect effect does not include zero; in this case, the interval excludes zero, so the indirect effect is significant.

How is partial mediation distinguished from full mediation in this workflow?

Full mediation would mean the direct effect C′ is not significant once the mediator is included, implying culture affects performance only through commitment. Partial mediation occurs when both the indirect effect (a×b) is significant and the direct effect C′ is also significant. Here, C′ is significant (reported as 0.2917), so the model indicates partial mediation.

What determines whether mediation is complementary or competitive?

The sign pattern of the direct and indirect effects. If the direct effect and indirect effect have the same sign (e.g., both positive), mediation is complementary. If one is positive and the other negative, it becomes competitive. In this model, all relevant coefficients are positive, so the mediation is complementary.

How should the results be reported at the end of a single-mediator PROCESS analysis?

A complete report lists the hypothesized relationships (culture→commitment→performance), the total effect, the direct effect (C′) with confidence intervals and t statistics, the indirect effect (a×b) with bootstrapped confidence intervals and t statistics, and the mediation conclusion (here: partial, complementary mediation).

Review Questions

  1. If C′ were non-significant while the bootstrapped indirect effect remained significant, what mediation type would that imply?
  2. Given a and b, how do you compute the indirect effect, and how does that relate to the total effect?
  3. What specific statistical criterion (in terms of confidence intervals) is used to decide whether the indirect effect is significant?

Key Points

  1. 1

    Use Hayes PROCESS Macro Model 4 to test mediation with one mediator by estimating paths X→M (a), M→Y (b), and X→Y controlling for M (C′).

  2. 2

    Compute the indirect effect as a×b and the total effect as C′ + (a×b).

  3. 3

    Confirm mediation by checking bootstrapped confidence intervals for the indirect effect; significance requires the interval to exclude zero.

  4. 4

    Classify mediation as full when C′ is not significant, and partial when C′ remains significant alongside a significant indirect effect.

  5. 5

    Determine whether mediation is complementary or competitive by comparing the signs of the direct and indirect effects.

  6. 6

    In this application, culture significantly predicts commitment and commitment significantly predicts organizational performance, producing a significant indirect effect of about 0.2736.

  7. 7

    Because both the indirect effect and the direct effect are significant, the culture→performance relationship is partial mediation through commitment and is complementary (positive direct and indirect effects).

Highlights

Culture’s effect on organizational performance splits into a direct component (C′ = 0.2917) and an indirect component through commitment (a×b ≈ 0.2736).
Bootstrapped confidence intervals for the indirect effect exclude zero, establishing a significant mediation pathway.
The direct effect remains significant after including commitment, so the model indicates partial mediation rather than full mediation.
All key coefficients are positive, so the mediation is complementary (direct and indirect effects move in the same direction).

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